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For buyers angling to get on the wait list for Ford Motor Co.F1.95% ’s new GT super car, having enough in the bank to cover the roughly $450,000 asking price isn’t enough. They also need to convince the company they are ready to drive.

In a rare move for the domestic auto industry, the Dearborn, Mich., auto maker is taking applications for the latest iteration of its mid-engine sports car. Ford will produce only 250 a year, but the company doesn’t want them collecting dust in garages.

The No. 2 U.S. car maker opened up the application process early Wednesday morning. The move comes about two weeks after Tesla Motors Inc. began taking $1,000 deposits for the Model 3, a much less expensive electric sedan that will bow next year.

To get a GT, candidates must lay out enthusiast credentials. If they have owned a previous-generation GT, for instance, Ford wants to know how many miles on that car’s odometer.

Prospects also have the chance to plead their case in writing and add supporting material, such as video and social media posts, that show dedication.

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“We really want to find those customers who will use this car and drive this car and be true ambassadors for Ford,” said Henry Ford III, great-great grandson of founder Henry Ford and global marketing manager for Ford’s performance division. Mr. Ford spoke to The Wall Street Journal in a podcast.

The reservation deadline for the first two years of production is May 12. Tesla’s Model collected 300,000 refundable deposits reservations in the first week of reservations—but that car is aiming for the mass market.

Ford’s application process “is the velvet rope line at the incredibly trendy club,” said Dave Kinney, who publishes the price guide for Hagerty Insurance Agency LLC, the largest insurer of classic and collector’s cars in the U.S. “For a lot of people, it’s very appealing.”

This latest GT, to be built with carbon fiber body panels and a 600-horsepower engine, made a big splash in 2015 at the Detroit auto show. The company had discontinued a prior edition it had started selling in 2004, and it backed away from investing in its gaudiest models during the financial crisis amid a cash shortage.

It isn’t uncommon for high-end cars to have lengthy wait lists or aim for handpicked clientele. Italy’s FerrariRACE1.48% NV, a sports car maker capping annual output at about 7,000, has multiyear waits and often allocates models based on how many Ferraris a buyer has purchased already.

The GT nameplate dates back to the 1960s, when the GT40 bolstered Ford’s racing chops by sweeping the 24 hours of LeMans. Original GT40s routinely sell for more than $1 million.

Ford revived the GT about a decade ago. It was designed to be an American-made, mid-engine supercar rivaling European exotics like Ferrari and Lamborghini SpA, but with a much lower price tag.

Early in its production run, demand was strong with the car selling over its $150,000 list price. Sales cooled, however after the initial rush.

Several years later, however, the GT is considered a favorite among collectors. Prices for low-mileage used models began to soar in late 2012, and today the average 2005-06 Ford GT is worth more than $250,000, according to Hagerty.

Karl Brauer, a 2005 Ford GT owner and senior analyst for car-research firm Kelley Blue Book, wasted no time to put in his application for the new one.

When he bought his first GT, it took three-and-a-half years for the company to fill his order.

Paying $165,000 originally, he estimates the car is worth about $230,000 with 28,000 miles on the odometer. He argues he’s the type of person Ford is looking for in an owner: someone who will drive the car and show it off.

All too often these kinds of cars are kept locked away in a garage somewhere as if they’re a trophy, Mr. Brauer said.

“[Ford is] trying to prevent them from becoming objects of the super wealthy to be stored away,” Mr. Brauer added. “It’s not a statement car if it sits under a cover.”

Christina Rogers at christina.rogers@wsj.com and Gautham Nagesh at gautham.nagesh@wsj.com